square of opposition

These relationships are the basis of the well-known Square of opposition.

These four concepts are related to each other in a manner exactly analogous to Aristotle's square of opposition.

It is an extension of Aristotle's square of opposition.

Aristotle's original square of opposition, however, does not lack existential import:

A notable philosopher with works in logic, he was also the responsible for the creation of the Square of opposition.

Of the Aristotelian square of opposition, only the contradictory relationships remain intact.

Chapter 7 is at the origin of the square of opposition (or logical square).

The square of opposition has been extended to a logical hexagon which includes the relationships of six statements.

The hypothetical viewpoint has the effect of removing some of the relations present in the traditional square of opposition.

The law holds for the A and E propositions of the Aristotelian square of opposition.

Notable is his use of Aristotelian notions such as the Square of Oppositions, and syllogistic logic in a modern semantic/pragmatic setting.

The square of opposition, under this Boolean set of assumptions, is often called the modern Square of opposition.

Greek investigations resulted in the so-called square of opposition, which codifies the logical relations among the different forms; for example, that an A-statement is contradictory to an O-statement.

"Aristotle's Non-Logical Works and the Square of Oppositions in Semiotics," Logica Universalis.

In the Stanford Encyclopedia of Philosophy article, "The Traditional Square of Opposition", Terence Parsons explains:

(c) What existential imports must the forms AaB, AeB, AiB and AoB have for the square of opposition be valid?

It has been put forth by Lithuanian linguist and semiotician Algirdas Julien Greimas, and was derived from Aristotle's logical square or square of opposition.

For classical logics, it is generally possible to reexpress the question of the validity of a formula to one involving satisfiability, because of the relationships between the concepts expressed in the above square of opposition.

In the modern square of opposition, A and O claims are contradictories, as are E and I, but all other forms of opposition cease to hold; there are no contraries, subcontraries, or subalterns.

In the system of Aristotelian logic, the square of opposition is a diagram representing the different ways in which each of the four propositions of the system is logically related ('opposed') to each of the others.

Immanuel Kant (1724-1804) defined his typology by a duality of the beautiful and sublime, and concluded it was possible to represent the four temperaments with a square of opposition using the presence or absence of the two attributes.

Gottlob Frege's Begriffsschrift also presents a square of oppositions, organised in an almost identical manner to the classical square, showing the contradictories, subalternates and contraries between four formulae constructed from universal quantification, negation and implication.

Given a type E statement, from the traditional square of opposition, "No S are P.", one can make the immediate inference that "No P are S" which is the converse of the given statement.

Consequently the four forms AaB, AeB, AiB and AoB can be represented in first order predicate in every combination of existential import, so that it can establish which construal, if any, preserves the square of opposition and the validly of the traditionally valid syllogism.